Publicly, the company has decried Kraft's $143 billion buyout offer as lacking merit and said there was no basis for further talks.

Behind the scenes, Unilever executives have fretted over Kraft's penchant for slashing costs and lack of vision for cultivating brands, according to people familiar with the situation. Kraft also lacks experience managing home and personal-care businesses, which account for about 60 percent of Unilever's revenue, they said.

Though Unilever publicly rejected the $50-a-share bid on Friday, Kraft has said it's still pursuing a deal. The prospect of both reaching an agreement sent shares of Unilever soaring 13 percent to a record high. The Anglo-Dutch company, which makes Hellmann's mayonnaise and Dove soap, is now valued at more than $142 billion.

The rally makes it more likely that Kraft will increase its offer, a person with knowledge of the bidder's deliberations. Shares of Kraft also jumped on the news, climbing 11 percent to $96.65. That values the food giant at $117.6 billion. An acquisition of Unilever would depend on financing from Kraft's largest investor, Berkshire Hathaway, a separate person familiar with the situation said.

Against that backdrop, Unilever is trying to convince investors that a deal wouldn't make sense. The company has been speaking to shareholders about why it should remain a stand-alone business, arguing that there aren't many synergies between the two entities, said people with knowledge of the matter.

The unsolicited approach from Kraft took Unilever by surprise, they said. Executives didn't expect an offer from Kraft because they see the companies as too different, according to the people. Unilever has less of a focus on food, and it's spent recent years acquiring upstart brands that appeal to millennials. That includes Dollar Shave Club and Seventh Generation.

At issue is whether Unilever's diverse investor base will see Kraft as a strategic fit. BlackRock is its largest shareholder, with a roughly 8 percent stake.

Under U.K. takeover rules, Kraft has just under a month to make a firm bid - or else it has to walk away for six months.